Decide whether the sequence can be represented perfectly by a linear or a quadratic model. If so, then find the model.

Firstly we need to determine whether the series is linear or quadratic. A linear sequence is a sequence of numbers in which there is a first difference between any consecutive terms is constant. However, a quadratic sequence is a sequence of numbers in which there is a second difference between any consecutive terms is constant. 

Now let's determine if the above sequence is linear or quadratic. 

Lets begin by finding the first difference: 

Firstly we need to determine whether the series is linear or quadratic. A linear sequence is a sequence of numbers in which there is a first difference between any consecutive terms is constant. However, a quadratic sequence is a sequence of numbers in which there is a second difference between any consecutive terms is constant. 

Now let's determine if the above sequence is linear or quadratic. 

Lets begin by finding the first difference: 

From above we can see we have a constant number for the first difference, hence our sequence is linear.

Now let's determine the model of this sequence. The equation of a linear sequence is as follows: 

Where 

T_n = Value of the term in sequence

a = first number of sequence

d = common difference (first difference)

n = term number 

Now let's substitute values into the above equation: 

The model is simplified to: 

Now let's double check our model using terms 1, 3 and 6: 

Summary: 

The sequence is linear. 

Model: 

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